A new approach for indexing powder diffraction data based on whole-profile fitting and global optimization using a genetic algorithm

This paper describes a new technique for indexing powder diffraction data. The lattice parameters (unit-cell dimensions) {a,b,c,α,β,γ} define the parameter space of the problem, and the aim is to find the optimal lattice parameters for a given experimental powder diffraction pattern. Conventional methods for indexing consider the measured positions of a limited number of peak maxima, whereas this new approach considers the whole powder diffraction profile. This new strategy offers several advantages, which are discussed fully. In this approach, the quality of a given set of lattice parameters is determined from the profile R-factor, R_wp, obtained following a Le Bail-type fit of the intensity profile. To find the correct lattice parameters (i.e. the global minimum in R_wp), a genetic algorithm has been used to explore the R_wp(a,b,c,α,β,γ) hypersurface. (Other methods for global minimization, such as Monte Carlo and simulated annealing, may also be effective.) Initially, a number of trial sets of lattice parameters are generated at random, and this `population' is then allowed to evolve subject to well defined evolutionary procedures for mating, mutation and natural selection (the fitness of each member of the population is determined from its value of R_wp). Examples are presented to demonstrate the success and underline the potential of this new approach for indexing powder diffraction data.